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Chapter 8: Q.8.4 (page 453)

Refer back to the pizza-delivery Try It exercise. The population standard deviation is six minutes and the sample mean delivery time is 36minutes. Use a sample size of 20. Find a95% confidence interval estimate for the true mean pizza delivery time

Short Answer

Expert verified

The interval estimate for the true mean pizza delivery time is (33.37,38.63)

Step by step solution

01

Given Information

Given the data that,

standard deviation is six minutes s and the sample mean delivery time is 36 minutes. Use a sample size of 20.

02

Explanation

The sample mean is36minutes, that is,x炉=36

The random sample of20pizza delivery restaurants, that is,n=20

The standard deviation is6, that is,蟽=6

03

Explanation

Now, using the procedures below, compute the confidence interval using a Ti-83 calculator.

Press STAT and use the arrow (?) to TESTS

Now press the arrow (鈫�)to 7: Zinterval and press enter

Then use the arrow (鈫�)to STATS and press enter

Now press the arrow (?) and enter the inputs as shown below

Now press the arrow (?) to the calculator and press enter. The output is given below,

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Most popular questions from this chapter

A random survey of enrollment at 35 community colleges across the United States yielded the following figures:

6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000;

9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080;

11,622. Assume the underlying population is normal.

a. i.x- = __________

ii. sx = __________

iii. n = __________

iv. n 鈥� 1 = __________

b. Define the random variables X and X-in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United

States.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600students and finds that 480are against the new legislation.

a. Compute a 90% confidence interval for the true percent of students who are against the new legislation, and interpret the confidence interval.

b.In a sample of 300students,68% said they own an iPod and a smartphone. Compute a 97% confidence interval for the true percent of students who own an iPod and a smartphone.

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709randomly selected adults, 315identified themselves as Latinos, 323identified themselves as blacks, 254identified themselves as Asians, and 779identified themselves as whites. In this survey, 86%of blacks said that they would welcome a white person into their families. Among Asians, 77%would welcome a white person into their families, 71%would welcome a Latino, and 66%would welcome a black person.

a. We are interested in finding the 95%confidence interval for the percent of all black adults who would welcome a white person into their families. Define the random variables Xand P', in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95%confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?

Suppose that an accounting firm does a study to determine the time needed to complete one person鈥檚 tax forms. It

randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The

population distribution is assumed to be normal.

a. I. X=________

ii. 蟽 =________

iii. n =________

b. In words, define the random variables X and X

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 90% confidence interval for the population mean time to complete the tax forms.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey,

what changes should it make?

f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to

the level of confidence? Why?

g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to

within one hour. How would the number of people the firm surveys change? Why?
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